I’m trying for a while now to remove completely the custom header.
but because twentytwelve is using it withrequire( get_template_directory() . '/inc/custom-header.php' );
I couldn’t just do the remove_theme_support() trick.
creating that directory with an empty custom_header.php in the child theme didn’t work out, either.
same as trying to remove the function called in the custom_header templateremove_action( 'after_setup_theme', 'twentytwelve_custom_header_setup', 11);
in different variations. no success 🙁